I usually put blanket or fabric.
My son works at UPS and is part of the HazMat Response Team, which deals with spills and breakage. I strongly recommend you wrap the quilt in waterproof plastic of some kind, and put your return address and the ship-to address clearly inside the box, in case the box gets wet or damaged. It's amazing how many people do not package their liquids very well, packages break and leak on other packages.